A235538 -id:A235538 - cp's OEIS frontend

A235539 Table with A235538 as first row, and k-th difference of A235538 as (k+1)-th row, read by antidiagonals.

1, 3, 2, 9, 6, 4, 26, 17, 11, 7, 5, -21, -38, -49, -56, 13, 8, 29, 67, 116, 172, 31, 18, 10, -19, -86, -202, -374, 15, -16, -34, -44, -25, 61, 263, 637, 27, 12, 28, 62, 106, 131, 70, -193, -830, 81, 54, 42, 14, -48, -154, -285, -355, -162, 668, 22, -59, -113

Offset: 1

Paul Tek, Jan 12 2014

All terms are distinct in absolute value.

			The table begins:
+---+---+---+---+---+
| 1 | 3 | 9 | 26| 5 | ...
+-+-+-+-+-+-+-+-+-+-+
  | 2 | 6 | 17|-21| ...
  +-+-+-+-+-+-+-+-+
    | 4 | 11|-38| ...
    +-+-+-+-+-+-+
      | 7 |-49| ...
      +-+-+-+-+
        |-56| ...
        +---+

Paul Tek, Table of n, a(n) for n = 1..5050
Paul Tek, PERL program for this sequence

Cf. A235538.

Perl
```
See Link section.
```

T(1,n) = A235538(k) for any k>0.

T(n+1,k) = T(n,k+1) - T(n,k) for any n>0 and k>0.

A327460 Lexicographically earliest infinite sequence of distinct positive integers such that for every k >= 1, all the k(k+1)/2 numbers in the triangle of differences of the first k terms are distinct.

Original entry on oeis.org

1, 3, 9, 5, 12, 10, 23, 8, 22, 17, 42, 16, 43, 20, 38, 26, 45, 32, 65, 28, 64, 39, 76, 34, 81, 48, 98, 40, 92, 54, 109, 60, 116, 51, 114, 58, 117, 70, 136, 67, 135, 71, 145, 72, 147, 69, 146, 80, 164, 87, 166, 82, 170, 108, 198, 101

Offset: 1

N. J. A. Sloane, Sep 25 2019

This is an infinite version of A327762. The first 55 terms are the same as in A327762.
Inspired by A327743.
The usual topological arguments show that there IS a sequence satisfying the definition. So far, the terms of A327460 lie on two roughly straight lines, of slopes about 1.75 and 3.5: see A328069, A328070. - N. J. A. Sloane, Oct 07 2019
If only the first differences are constrained, one gets the classical Mian-Chowla sequence A005282. - M. F. Hasler, Oct 09 2019. See also another classic, A005228, and A328190. - N. J. A. Sloane, Nov 01 2019

			The difference triangle of the first k=8 terms of the sequence is
     1,    3,    9,   5,  12,  10,  23, 8, ...
     2,    6,   -4,   7,  -2,  13, -15, ...
     4,  -10,   11,  -9,  15, -28, ...
   -14,   21,  -20,  24, -43, ...
    35,  -41,   44, -67, ...
   -76,   85, -111, ...
   161, -196, ...
  -357, ...
All 8*9/2 = 36 numbers are distinct.

Peter Kagey, Table of n, a(n) for n = 1..4000

Cf. A005228, A005282, A035313, A327743, A327762, A328190.
See also A327458 (differences), A328066 (sorted), A328067, A328068 (complement), A328069 and A328070 (bisections), A328071; A235538 (absolute differences distinct).
The inverse binomial transform is A327459.

cp's OEIS Frontend

A235539 Table with A235538 as first row, and k-th difference of A235538 as (k+1)-th row, read by antidiagonals.

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